Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2 (B) 4 (C) 8 (D) 20 (E) 45

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

We can rewrite the given equality as \(s = 64t + 0.12t\). The divider is t, the quotient is 64. The remainder is \(0.12t\) (it is less than t) and it is an integer, being equal to \(s-64t\). Since \(0.12t=\frac{3}{25} t\), it follows that t should be a multiple of 25, so \(t=25n\), for some positive integer n. Therefore, the remainder is \(3n\), or a multiple of 3. The only answer that is a multiple of 3 is 45.

Answer: E
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]

Show Tags

02 Jul 2012, 02:55

1

This post received KUDOS

i dont know if this method is correct or not, would need expert check s/t = 64.12 = 64+12/100 = 64+3/25 i got 3, and in the options the multiple of is 45

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2 (B) 4 (C) 8 (D) 20 (E) 45

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

If s and t are positive integers such that s/t = 64.12 which [#permalink]

Show Tags

18 Aug 2012, 05:50

10

This post received KUDOS

1

This post was BOOKMARKED

Shortcut for this question:- 64.12 = 64 + 12/100 Now focus on remainder part which is 12/100= 3/25 Because 3 represents some fraction (ratio) of remainder , the remainder must be a multiple of 3. only 45 is a multiple of 3.

Time taken app20sec

Waiting for few kudos
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

which of the following could be the remainder when s is divided by t?

(A) 2 (B) 4 (C) 8 (D) 20 (E) 45

s/t = 64.12, => s = t*64.12 => s = 64t + t*.12 So, when s is divided by t then we will get t*.12 as reminder (as t*.12 will be less than t) Now t is an integer and .12 is 12*.01 which means it is 3*something So, only answer choices which are multiple of 3 are contenders.

If s and t are positive integers such that s/t = 64.12, which of [#permalink]

Show Tags

26 Dec 2012, 23:15

9

This post received KUDOS

3

This post was BOOKMARKED

\(\frac{S}{t} = 64 + .12\) \(S = 64t + .12t\)

The remainder is equal to .12t.

R = .12t R/.12 = t

We have to look for R where R/.12 is an integer.

A)2/.12 = 200/12 is not an integer B)4/.12 = 400/12 = 100/3 is not an integer C) 8/.12 = 800/12 = 400/6 = 200/3 is not an integer D) also not E) 45/12 = 4500/12 = 1500/4 = 15*25 is an integer

If s and t are positive integers such that s/t = 64.12 which [#permalink]

Show Tags

23 Jun 2014, 03:25

Bunuel wrote:

SOLUTION

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2 (B) 4 (C) 8 (D) 20 (E) 45

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

I did not understand why r must be a multiple of 3? From answer choice E 45 is 15 times 3 (a multiple of 3) does that mean t will be 15 times 25?

If s and t are positive integers such that s/t = 64.12 which [#permalink]

Show Tags

23 Jun 2014, 03:41

3

This post received KUDOS

1

This post was BOOKMARKED

nehamodak wrote:

Bunuel wrote:

SOLUTION

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2 (B) 4 (C) 8 (D) 20 (E) 45

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

I did not understand why r must be a multiple of 3? From answer choice E 45 is 15 times 3 (a multiple of 3) does that mean t will be 15 times 25?

Because \(\frac{3}{25}\)cannot be simplified further (say factorised further)

\(\frac{3}{25}= \frac{3*15}{25*15}= \frac{45}{25*15}\) ... That is possible
_________________

WE: Project Management (Non-Profit and Government)

Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]

Show Tags

01 Mar 2015, 00:31

Bunuel wrote:

SOLUTION

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2 (B) 4 (C) 8 (D) 20 (E) 45

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

If the question had been which of the following cannot be the remainder. Then can we use the propertry that Remainder must be divisibe by 25 as well???

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2 (B) 4 (C) 8 (D) 20 (E) 45

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

If the question had been which of the following cannot be the remainder. Then can we use the propertry that Remainder must be divisibe by 25 as well???

Dear Ankush

Good to see you here on GC!

Here's the answer to your question:

It is not necessary for the remainder to be divisible by 25.

Let's look at this in terms of constraints:

Constraint 1: The remainder is always a non-negative integer.

From the equation

\(\frac{r}{t}=\frac{3}{25}\), we get that

r=\(\frac{3t}{25}\)

From constraint 1, we see that

\(\frac{3t}{25}\) must be a non-negative integer.

This means either t = 0 or t is a multiple of 25.

But t cannot be equal to 0 because then the expression \(\frac{s}{t}\) becomes undefined

This means, t is a multiple of 25.

Constraint 2: The question states that t is a positive integer.

As explained in the post I made just above, this means \(\frac{25r}{3}\) is a positive integer, which leads you to the inference that r is a multiple of 3.

So, the bottom-line is that the only 2 inferences that we can conclusively draw from the given information is that:

i) t is a multiple of 25 and ii) r is a multiple of 3